Answer:
105.2 ft²
Step-by-step explanation:
The diameter of the base of the cone is 6 ft which means its radius is:
r = d / 2 = 6 / 2 = 3 ft
Its height, h, is 7.6 ft.
The surface area of a cone is given as:
A = pi * r(r + √(h² + r²))
Therefore:
A = pi * 3(3 + √(7.6² + 3²))
A = pi * 3(3 + √(57.76 + 9))
A = pi * 3(3 + √(66.76))
A = 9.42(3 + 8.17)
A = 9.42 * 11.17 = 105.2214 ft²
Approximating to the nearest 10th, the surface area of the cone is 105.2 ft².
Felicia makes \frac{1}{2}
2
1
gallon of fruit punch. She pours an equal amount into 8 glasses.
What fraction of a gallon fruit punch is in each glass?
Question:
Felicia makes ½ gallon of fruit punch. She pours an equal amount into 8 glasses.
What fraction of a gallon fruit punch is in each glass?
Answer:
The fraction of a gallon fruit punch is in each glass is 1/16
Step-by-step explanation:
Given
Size of fruit punch = ½ gallon
Number of glass = 8
Required
Fraction of a gallon fruit punch is in each glass?
To solve this question, the following assumption has to be made.
- The 8 glass cups are of equal sizes.
Having said that;
The interpretation of the question is that, the fruit is evenly distributed into the 8 glass cups.
Mathematically, the size of the fruit punch will be divided by the number of glass cups.
So, we have
Fraction = ½ ÷ 8 (convert ÷ to *)
Fraction = ½ * ⅛
Fraction = 1/16
Hence, the fraction of a gallon fruit punch is in each glass is 1/16
Final answer:
To find the fraction of a gallon of fruit punch in each glass, divide 1/2 gallon by 8. This results in each glass containing 1/16 of a gallon of fruit punch.
Explanation:
The student asked how to find the fraction of a gallon of fruit punch in each glass if Felicia makes ½ gallon of fruit punch and pours an equal amount into 8 glasses. To answer this question, you need to perform a division of the total amount by the number of glasses. Given that Felicia has ½ gallon, which is the same as 2/4, we can divide this by 8 to find the amount in each glass.
Step-by-step solution:
Start with the fraction of a gallon Felicia has: ½ gallon.
Convert ½ to fourths to make the division easier: ½ = 2/4 gallons.
Since there are 8 glasses, divide 2/4 by 8. This is done by multiplying the denominator by 8:
(2/4) × (1/8) = 2/32.
Simplify the fraction by dividing numerator and denominator by the common factor of 2: 2/32 = 1/16.
Therefore, each glass contains 1/16 of a gallon of fruit punch.
Find the area of the section of the basketball court that is showh.
Round to the nearest tenth.
Answer:
Area is Base multipled by your height, so fro that particular section, it's quite a simple equation! :D
Step-by-step explanation:
Let's identify our sides. 39ft6in is our HEIGHT, and 5ft3in is our BASE.
- 39ft and 6in is a total of: 472 inches. 472 inches is 39.3ft
- 5ft and 3in is a total of: 63 inches. 63 inches is 5.3ft
Now that we know this, we can plug it in depending on the unit you need to find! Let's assume it's feet?
The Equation Completed: 5.3 × 39.3 = 208.29, which rounds to 208.3!
FINAL ANSWER: 208.3ft
What shapes can be cross sections of the rectangular pyramid?
A slice parallel to the base will take the shape of a .
A slice perpendicular to the base and through the top vertex will take the shape of a .
A slice perpendicular to the base and not through the top vertex will take the shape of a .
Answer:
What shapes can be cross sections of the rectangular pyramid?
A slice parallel to the base will take the shape of a
✔ rectangle
.
A slice perpendicular to the base and through the top vertex will take the shape of a
✔ triangle
.
A slice perpendicular to the base and not through the top vertex will take the shape of a
✔ trapezoid
.
A slice parallel to the base will take the shape of the rectangle. A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".
A slice perpendicular to the base and through the top vertex will take the shape of a .
A slice perpendicular to the base and not through the top vertex will take the shape of a .
Take a rectangle and the base. Now take four triangles such that each of them is connected to one-one side of the base rectangle and when they are taken together, they form a closed object.
That shape is called a rectangular pyramid.
A slice parallel to the base will take the shape of a "rectangle"
A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".
A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".
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Which geometric series converges?
0.02+0.02+0.02+0.02+...
4+0.08 +0.0016+0.000032+
4+80+ 1.600+ 32,000+.
0.02+0.04+0.08+0.16+.
Answer:
4+0.08 +0.0016+0.000032+ ....
Step-by-step explanation:
a+ar+ar²+ar³+ar⁴+…
the geometric series converges if |r| < 1
The geometric series converges:
4+0.08 +0.0016+0.000032+ ....
0.08=4*0.02
0.0016=4*(0.02)²
0.000032=4*(0.02)³
r=0.02<1
The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.
What is the geometric series?A geometric series is one where each pair of subsequent terms' ratios is a fixed function of the accumulation index. The ratio is a rational function of the accumulation index in a more comprehensive sense. creates what is known as a hypergeometric sequence.
If the common ratio is the same throughout the series, then the series is known as geometric series.
If the common ratio is less than one, then the series is known as convergence.
Let's check all the options, then we have
A. 0.02+0.02+0.02+0.02+...
Then the common ratio is given as,
r = 0.02 / 2 = 0.02 / 0.02
r = 1 = 1
B. 4+0.08 +0.0016+0.000032+....
Then the common ratio is given as,
r = 0.08 / 4 = 0.0016 / 0.08
r = 0.02 = 0.02
C. 4+80+ 1,600+ 32,000+.....
Then the common ratio is given as,
r = 80 / 4 = 1600 / 80
r = 20 = 20
D. 0.02+0.04+0.08+0.16+......
Then the common ratio is given as,
r = 0.04 / 0.02 = 0.08 / 0.04
r = 2 = 2
The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.
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what is the mean of the value set 13,19,22,20,31,16,25,30
Answer:
the mean is the midle one
we can get this by getting the average
add all of it and divide by how many it is
Chayton read a report that said the probability that a randomly selected American is left-handed is 14%.
He was curious how many left-handed students to expect in a class of 20 students.
He simulated 25 classes of 20 students where each student selected had a 0.14 probability of being left-
handed.
Chayton counted how many left-handed students were in each simulated class. Here are his results:
Answer:
P(2 or fewer left-handed) = 9/25 = 0.36
Step-by-step explanation:
From Chayton simulations, we can see that in 9 simulations there are 2 or fewer left-handed students in a class of 20 students. He simulated 25 classes of 20 students, then the probability to find 2 or fewer left-handed is: 9/25 = 0.36
Which of the following is the best approximation of the area of a circle whose diameter is 14 feet?
88 square feet
44 square feet
616 square feet
154 square feet
Josh bought a pizza with eight slices of pizza for $12. What is the cost of a slice of pizza? $12 $3 $1 $1.50
Answer:
$1.50
Step-by-step explanation:
12÷8=3/2 or 1.50
Answer: the answer would be 1$ and 50 cents
Step-by-step explanation:
Daniel's class has 30 students. In the class, 16 students are boys. Which decimal is equivalent to the fraction of the class that is boys?
Answer:
0.53333333333
Step-by-step explanation:
The fraction of the class that is boys is 16/30.Therefore, the decimal equivalent the fraction of boys in Daniel's class is 0.53.
Explanation:The fraction of the class that is boys is obtained by dividing the number of boys by the total number of students. In this case, there are 16 boys and 30 students in total. The fraction is therefore 16/30.
To write this fraction as a decimal, divide the numerator (16) by the denominator (30). The decimal equivalent of 16/30 is approximately 0.5333.
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Solve the equation. First estimate using the perfect square closest to 45. Then use a calculator. n2=45
Answer:22.5
Step-by-step explanation: just saying that is no the actual answer you still have to estimate it
The equation n² =45 is solved step by step. The nearest perfect squares, 36 and 49, are identified. Using a calculator, the square root of 45 is found to be approximately 6.708, satisfying the equation.
let's go through the steps to solve n² = 45 in detail:
Step 1: Find the Perfect Squares
The closest perfect squares to 45 are 6² = 36 and
7² = 49.
Since 45 is between 6² and 7², we'll use these values as reference.
Calculate the Square Root
We'll use a calculator to find the square root of 45.
√45 ≈ 6.708203932499369
So, the square root of 45 is approximately 6.708203932499369.
Step 3: Solve for n
Since we're looking for n² = 45, we have √n = 45.
Plugging in the calculated square root:
√n = 45
n ≈ 6.708203932499369
Thus, the approximate value of n that satisfies the equation n² = 45 is n ≈ 6.708.
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CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION
Answer:
The value of DC is 66.34.
Step-by-step explanation:
The triangles ABC and DCA are right angled triangles.
The straight line AC is a bisector for angles C and A.
The measure of ∠C is 30°.
Then the measure of angles BCA and ACD will be 15° each.
The measure of angle DAB is 150°.
Then the measure of angles DAC and BAC will be 75° each.
Now consider the right angled triangle ABC.
The measure of side AC is:
[tex]AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}[/tex]
Consider the right angled triangle DCA.
The angle DAC measure 75°.
Using the trigonometric identities compute the value of Perpendicular DC as follows:
[tex]tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34[/tex]
Thus, the value of DC is 66.34.
a 5cm x 11cm rectangle sits inside a circle with a radius of 12cm
what is the area of the shaded region? the shaded region is the circle - the rectangle inside it.
Answer: 397.39 cm2
Step-by-step explanation:
Hi, first we have to calculate the area of the circle:
Area of a circle = π x r^2
Replacing with the values:
A(C) =π x 12^2 = 452.39cm2
Now, we have to calculate the rectangle area:
Rectangle area = width x length = 5 x11 = 55cm2
Finally, since the shaded region is the circle and the rectangle is inside of it, we have to subtract the area of the rectangle to the area of the circle:
452.39 -55 = 397.39 cm2
Feel free to ask for more if needed or if you did not understand something.
Answer:
397.39
Step-by-step explanation:
extras...
4x - 5x + 9 = 5x - 9
Answer:
= 3
Step-by-step explanation:
4 − 5 + 9 = 5 − 9
− + 9 = 5 − 9
i hope this helps<3
:)
The value of solution of expression is,
⇒ x = 3
We have to given that;
Mathematical expression is,
⇒ 4x - 5x + 9 = 5x - 9
Now, We can simplify as;
⇒ 4x - 5x + 9 = 5x - 9
⇒ - x + 9 = 5x - 9
⇒ 9 + 9 = 5x + x
⇒ 18 = 6x
⇒ 6x = 18
⇒ x = 18 / 6
⇒ x = 3
Thus, The value of solution of expression is,
⇒ x = 3
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In a sequence, the first term is 8 and the common difference is -5. The fifth term in this sequence is
Answer:
5th term is -12
Step-by-step explanation:
First term is 8, which means 0th term is 13.
You can use the equation to find the nth term: y = -5(x) + 13
y = -5(5) + 13
y = -25 +13
y= -12
The fifth term in the sequence is -12.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
First term = 8
Common difference = -5
We can consider the sequence to be an arithmetic sequence.
Now,
a = 8
Second term.
= a + (n - 1)d
= 8 + (2 - 1)(-5)
= 8 - 5
= 3
Third term.
= 8 + (3 - 1) (-5)
= 8 + 2 x -5
= 8 - 10
= -2
Fourth term.
= 8 + (4 - 1) x -5
= 8 + 3 x -5
= 8 - 15
= -7
Fifth term.
= 8 + (5 - 1) x -5
= 8 + 4 x -5
= 8 - 20
= -12
Thus,
The fifth term of the sequence is -12.
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Suppose you first want to eliminate the fraction in 4n=1/2(2n-12). What would your first step be? Is -2 still the solution when you start by eliminating the fraction first? Explain
Answer:
Step-by-step explanation:
Recognize that the (1/2) in 4n=1/2(2n-12) is a coefficient, the coefficient of the (2n - 12) term.
Thus, multiply both sides of this equation 4n=1/2(2n-12) by 2, to obtain:
8n = 2n - 12
Combining like terms, we get 6n = -12, so that n = -2.
Multiplying both sides of the equation by a constant does not in any way affect your ability to find a solution and does not change the solution.
Becker and Kayla are members of the school chess team. They record the number of games they each play for 10 days. The data are shown. Becker: 5,2,4,1,1,4,5,3,2,1 Kayla: 2,3,1,1,4,1,5,3,5,5 Based on the data, which estimate represents the mean number of games chess team members play per day?
Answer:
2.9
Step-by-step explanation:
The mean is the average of the date It is surprisingly easy to calculate: add up all the data, then divide by how many data points there are.
Becker's data added up is 28. Kayla's data added up is 30. The total amount is 58.
The amount of data points are 20.
58/20 = 2.9
Hope this helps!
The mean number of games chess team members play per day is 2.9
How to find mean of the dataBecker = 5,2,4,1,1,4,5,3,2,1
= (5 + 2 + 4 + 1 + 1 + 4 + 5 + 3 + 2 + 1) / 10
Mean average = 28 / 10
= 2.8
Kayla = 2,3,1,1,4,1,5,3,5,5
= (2 + 3 + 1 + 1 + 4 + 1 + 5 + 3 + 5 + 5) / 10
= 30 / 10
= 3
Total = Becker + Kayla
= 2.8 + 3
= 5.8
Mean average = 5.8 / 2
= 2.9
Therefore, the mean number of games chess team members play per day is 2.9
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Martin is using unit cubes to build a tower in the shape of a rectangular prism. A decripion of the tower is listed the bottom layer is made of 16 unit cubes. the bottom layer shape is in the shape of a square prism. 9 more equal layers of unit cubes are added on the top of the bottom layer. what is the total volume in cubic units of the completed tower
Answer:
Volume of the completes tower = 160 units³
Step-by-step explanation:
Martin is using unit cubes to build a tower in the shape of rectangular prism.
Bottom layer of the prism is in the square shape.
Since number of unit cubes used in the bottom layer = 16
So, one side of the square base will measure = √16 = 4 units
Therefore, Length = width = 4 units
On this base, additional layers added on the top = 9
Therefore, height of the tower = (9 + 1) = 10 units (each layer having 16 cubes)
Volume of the tower = Volume of the rectangular prism
= Length × width × height
= 4×4×10
= 160 cubic units.
Volume of the completed tower will be 160 cubic units.
The total volume in cubic units of the completed tower is 160 units³.
Calculation of the total volume;Since number of unit cubes used in the bottom layer = 16
So, one side of the square base should be
= √16 = 4 units
Now
Length = width = 4 units
The additional layers added on the top = 9
So, height of the tower = (9 + 1)
= 10 units
Now
Volume of the tower = Volume of the rectangular prism
= Length × width × height
= 4×4×10
= 160 cubic units.
hence, The total volume in cubic units of the completed tower is 160 units³.
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How does multiplying the variable of an absolute value function by a positive constant, k, affect the vertex of the function?
The vertex shifts up k units.
The vertex shifts to the right k units.
The vertex of the function doesn't change.
The vertex of the function changes from a minimum to a maximum or vice versa.
Answer:
C. The vertex of the function doesn't change.
What is the vertex of the quadratic function?
х) = (х – 8)(х – 4)
А. (-6,4)
В. (6-4)
с. (-4,8)
D. (4,8)
Answer:
The vertex is (6, -4)
Step-by-step explanation:
f(x) =(х – 8)(х – 4)
First find the zeros
0 = (х – 8)(х – 4)
0 = x-8 0 =x-4
x=8 x=4
The zeros are x=8 and x=4
The vertex is 1/2 way between the zeros
(8+4)/2 = 12/2 =6
To find the y value, substitute 6 into the function
f(6) = (6-8) (6-4)
= -2 (2) = -4
The vertex is (6, -4)
Algebraic Expression: The length of a rectangle is five inches less than triple the width. If the width is w inches, how long is the length of the rectangle?
Answer:
l=(3w-5) Inches
Step-by-step explanation:
Let the width of the rectangle =w inches
The length of a rectangle is five inches less than triple the width.
Let us break the statement down into parts.
Triple the width=3wFive inches less than triple the width =3w-5Therefore, the length of the rectangle, l= (3w-5) Inches
Use polynomial identities and number properties to calculate 25^3
Answer:
15625
Step-by-step explanation:
25^3
The base is 25 and the power is 3
That means we multiply 25 together 3 times
= 25*25*25 =15625
Answer:
15,625
Step-by-step explanation:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(20+5)³
20³ + 3(20²)(5) + 3(20)(5²) + 5³
8000 + 6000 + 1500 + 125
15625
How will a high outlier in a data set affect the mean and median?
O A. distribution skewed to the right, mean not effected, median skewed to the right
O B. distribution skewed to the right, mean pulled to the right, median not effected
O C. distribution skewed to the right, mean not effected, median not effected
OD. distribution skewed to the left, mean pulled to the left, median not effected
Answer:
B. distribution skewed to the right, mean pulled to the right, median not effected
Step-by-step explanation:
When a distribution is skewed to the right, it means that the data is positively skewed or has more positive numbers than negative numbers.
An outlier can affect the mean of a distribution since a high value outlier will make the mean be much higher than the median. In this case, since the distribution is positively skewed, a high outlier will pull the mean to the right (to higher positive values).
The high outlier in a data set affects the mean and median is
B. distribution skewed to the right, mean pulled to the right, median not effected
The reason why will a high outlier in a data set affect the mean and median?At the time When a distribution is skewed to the right, so it represents the data is positively skewed or it contains more positive numbers as compared to the negative numbers. An outlier can impact the mean of the distribution.
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I really don’t get this how do I do this:(?
Answer:
You are drawing a right triangle. So draw the two lines off of the right angle. Then write 5 along one line. That line is now BC, so you can start naming points and putting in lengths. Then, draw the hypotenuse (AB) going from the end of the line you were writing next to, to the other line. Make sure it is at least twice as long, because it is 13 long. Then, to find the length of the last line, square 13, and subtract 25 from it. Take that number and find it's square root. You should get 12, which is your answer.
Step-by-step explanation:
The length of the base of a square pyramid is 9 inches. The slant height is 12 inches. What is the surface area of the pyramid? A) 189 in2 B) 225 in2 C) 297 in2 D) 360 in2
Answer: C) 297 in2
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Surface area of a square pyramid (S) = 2 (length of the base) slant + length of the base ^2
S = 2bs + b^2
Replacing with the values given:
S = 2 (9) 12 + 9^2
S = 216 +81 = 297 square inches
Feel free to ask for more if needed or if you did not understand something.
Simplify.
3a + 2b - 8a + b
11a+ 3b
5a+3b
-5a+3b
-11a + 2b
A right triangle has side lengths 7, 24, and 25 as shown below.
Use these lengths to find cos A, tan A, and sinA.
cosA =
0
tan A =
0
co
B
sinA =
Answer: Cos A = 0.96, Tan A = 0.29 and Sin A = 0.28
Step-by-step explanation: The right angled triangle can be solved by applying the trigonometric ratios given a follows;
Sin A = opposite/hypotenuse
Cos A = adjacent/hypotenuse
Tan A = opposite/adjacent
In the triangle ABC, the side AB (25) is the hypotenuse [facing the right angle], the side CB (7) is the opposite [facing the reference angle A°] while the side AC (24) is the adjacent [line between the reference angle and the right angle].
Therefore, using angle A as the reference angle;
(a) Cos A = adjacent/hypotenuse
Cos A = AC/AB
Cos A = 24/25
Cos A = 0.96
(b) Tan A = opposite/adjacent
Tan A= CB/AC
Tan A = 7/24
Tan A = 0.29
(c) Sin A = opposite/hypotenuse
Sin A = CB/AB
Sin A = 7/25
Sin A = 0.28
A block of cheese has a volume of 187 cm3 and a mass of 140 g.
What is the density of the cheese in g/cm3 rounded to 2 decimal places?
Answer:
0.75 g/cm^3 to 2 decimal places.
Step-by-step explanation:
Density = mass / volume
= 140 / 182
= 0.7487 g/cm^3.
The density of the cheese is 0.75 [tex]g/cm^3[/tex].
The student has asked to calculate the density of a block of cheese with a given volume and mass. Density is defined as mass per unit volume and is calculated using the formula:
Density = Mass / Volume
To find the density of cheese:
Use the given mass of the cheese, which is 140 grams.
Divide the mass by the given volume of the cheese, which is 187 [tex]g/cm^3[/tex].
Perform the division to get the density in grams per cubic centimeter ( [tex]g/cm^3[/tex].)
The calculation is as follows:
Density = 140 g / 187 [tex]g/cm^3[/tex]= 0.7487 [tex]g/cm^3[/tex].
After rounding to two decimal places, the density of the cheese is 0.75 [tex]g/cm^3[/tex].
The table below represents Gerry's trip to school and back home. If the total time is 45 minutes, how far does Gerry live from school?
Chose the best equation to solve for x
Answer:
1) x/8+ x/16= 3/4 2) 4 miles
Step-by-step explanation:
The table is an illustration of distance, rates (speed) and time.
The best equation to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex].Gerry lives 4 miles from schoolFrom the question, we have:
[tex]t =45\ mins[/tex] --- total time spent
Convert to hours
[tex]t =\frac{45}{60}hr[/tex]
Reduce fraction
[tex]t =\frac{3}{4}hr[/tex]
The times spent to school and back home are given as:
[tex]t_1 = \frac x8[/tex]
[tex]t_2 = \frac x{16}[/tex]
So, we have:
[tex]t_1 + t_2 = t[/tex]
This gives:
[tex]\frac x8 + \frac x{16} = \frac 34[/tex]
Hence, the equation that can be used to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex]
Take LCM
[tex]\frac{2x + x}{16} = \frac 34[/tex]
[tex]\frac{3x}{16} = \frac 34[/tex]
Multiply through by 16
[tex]\frac{3x}{16}\times 16 = \frac 34 \times 16[/tex]
[tex]3x = 12[/tex]
Divide both sides by 3
[tex]x = 4[/tex]
The distance to school and back home are given as:
[tex]d_1 = d_2 = x[/tex]
So, we have:
[tex]d_1 = d_2 = 4[/tex]
This means that Gerry lives 4 miles from school
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Is this relation a function? Justify your answer.
No, the relation isn't a function. Though positive and balanced, one input has two outputs, violating the "one input, one output" rule.
No, the relation depicted in the image is not a function. While the relation does have the same number of x values as y values, and all the values are positive, a key characteristic of a function is missing.
For a relation to be a function, each input (represented by the x -value) must correspond to exactly one output (represented by the y -value).
In the image, we see that the input value 1 has two corresponding output values, 7 and 11. Since an input value cannot have multiple outputs, this relation is not a function.
So the answer is D. No, because two points with the same x -value have different y values.
Which would be a correct first step to solve the following system of linear equations using the elimination method? 2x+3y=6
-x+3y=15
A) Add the two equations together
B) Multiply the second equation by 2
C) Write the first equation in the form y=Mx+b
D) Multiply the second equation by -3
Step-by-step explanation:
2X alla seconda meno 3